64 lines
2.1 KiB
Java
64 lines
2.1 KiB
Java
/*
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The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.
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The first ten terms would be:
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1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
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Let us list the factors of the first seven triangle numbers:
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1: 1
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3: 1,3
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6: 1,2,3,6
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10: 1,2,5,10
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15: 1,3,5,15
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21: 1,3,7,21
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28: 1,2,4,7,14,28
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We can see that 28 is the first triangle number to have over five divisors.
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What is the value of the first triangle number to have over five hundred divisors?
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*/
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public class Problem_12 {
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/* returns the nth triangle number; that is, the sum of all the natural numbers less than, or equal to, n */
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public static int triangleNumber(int n) {
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int sum = 0;
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for (int i = 0; i <= n; i++)
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sum += i;
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return sum;
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}
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public static void main(String[] args) {
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long start = System.currentTimeMillis(); // start the stopwatch
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int j = 0; // j represents the jth triangle number
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int n = 0; // n represents the triangle number corresponding to j
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int numberOfDivisors = 0; // number of divisors for triangle number n
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while (numberOfDivisors <= 500) {
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// resets numberOfDivisors because it's now checking a new triangle number
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// and also sets n to be the next triangle number
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numberOfDivisors = 0;
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j++;
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n = triangleNumber(j);
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// for every number from 1 to the square root of this triangle number,
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// count the number of divisors
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for (int i = 1; i <= Math.sqrt(n); i++)
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if (n % i == 0)
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numberOfDivisors++;
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// 1 to the square root of the number holds exactly half of the divisors
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// so multiply it by 2 to include the other corresponding half
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numberOfDivisors *= 2;
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}
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long finish = System.currentTimeMillis(); // stop the stopwatch
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System.out.println(n);
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System.out.println("Time taken: " + (finish - start) + " milliseconds");
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}
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}
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